1. Field of the Invention
This invention relates to a method of and an apparatus for filtering an image, and more particularly to those for carrying out an image filtering in which an interpolation processing is carried out to increase the number of image signal components of a digital image signal.
2. Description of the Related Art
There have been known image recording apparatus such as laser printers, thermal printers and the like for recording a digital image in an actual size or to an enlarged or reduced scale. In such an image recording apparatus, a digital image signal obtained by sampling an analog image signal is subjected to a predetermined image processing, as required, for instance, to an interpolation processing in the case where the image is to be enlarged and then reproduced on an image recording medium.
When the density of the picture elements of the image signal is changed as disclosed, for instance, in Japanese Unexamined Patent Publication No. 2(1990)-13910, EP 753828 A2, U.S. Ser. No. 08/823,312 and/or the response of the image is adjusted as disclosed in U.S. Ser. No. 08/406,076 in order to reproduce an image more faithful to the original on the basis of an image signal obtained by sampling, a filtering processing is generally carried out on the image signal.
In such a filtering process the number of image signal components is increased by interpolation of values obtained by convolution integration using values of all the picture elements within the filter size (within the area covered with the filter) and the coefficient of the filter corresponding to each of the picture elements for the purpose of interpolation enlargement of the image or changing the density of picture elements.
Conventionally the convolution integration is carried out according to the following operation expression. ##EQU1##
The expression (1) is inclined to set the values of the interpolated picture elements so that continuity between the picture elements becomes smooth.
In the case where an analog image is read out by a scanner or the like, continuity of the image is high due to band limitation. To the contrast, when letters or patterns are inserted into a digital image, a discontinuous part or an edge appears in the image since band limitation is not effected. When such an edge is within the filter size, ringing artifact appears near the edge when the values of the interpolated picture elements are set by the convolution integration having the aforesaid inclination.
For example, when interpolation is carried out on an image signal made up of picture elements (sampling points on the original) whose values (values of image signal components representing the picture elements) are as shown by black dots (.circle-solid.) in FIG. 6A, it is ideal that the interpolated picture elements have values falling on the dotted line in FIG. 6A. However when the values of the interpolated picture elements are determined according to the aforesaid operation expression, the interpolated picture elements have values represented by white dots (.smallcircle.) in FIG. 6B and the output fluctuates to cause ringing.